Technically, these are all decoctions, and “decoction of tea (the plant)” has become just “tea”, which is now colloquially replaced “decoction”.

So in the sense I was using tea, as a replacement for “decoction”, coffee is a “tea”, insofar that the replaced word, “decoction”, boiled plant matter drink.

Language isn’t quite as black as white as we’d sometimes wish it was.

So you’re not wrong, per se, but neither am I.